How does German health insurance work for unemployed non-German partner moving here?

My wife is German and has private health insurance here due to her job as a teacher (she is beamtet, so the state pays for part of the private insurance). This is from the [Wiki](https://en.wikipedia.org/wiki/Beamter) page about her insurance –

* a special health plan, the Beihilfe, which covers 50% of most health care expenses for the Beamter, their spouse, and dependent children, with the Beamter being responsible for the remainder of the cover (usually achieved by taking out private health insurance)

I’ve moved here after we got married and we need to figure out the best way for me to be insured. I am happy with public insurance if that is cheaper.

We were told that it depends on my annual income whether I am eligible for public insurance or not. I moved here after a PhD and am currently looking for jobs. Does anyone else have experience with this?

by hlyj